BAPnP: A Barycentric Affine Invariant Linear Solver for Robust and Efficient Perspective-n-Point Pose Estimation

This repository contains the MATLAB simulations and C++ implementation for the paper:

"BAPnP: A Barycentric Affine Invariant Linear Solver for Robust and Efficient Perspective-$n$-Point Pose Estimation"

BAPnP is an efficient $O(n)$ solver that leverages geometry-guided base selection to maximize the reference basis volume, providing a reliable initialization for Gauss-Newton refinement, especially in quasi-planar configurations. It maintains 100% success rate down to strict coplanarity while executing in just $4.4,\mu s$ at $N=10$ in C++.

---

3. Supplementary Materials

supplementary.pdf in the repository root archives three reviewer-requested experiments that are not included in the main manuscript:

Section	Content	Description
§2	Localized Basis-Point Corruption	Pure-linear oDLT comparison under targeted basis-point noise (0--20 px)
§3	Minimal-Configuration Analysis	Performance of all 9 PnP methods at $N=4,5,6$ ($\sigma=3$ px)
§4	Extremal Outlier Injection	RANSAC-integrated comparison under 10%--50% synthetic periphery outliers

The C++ sources for the supplementary experiments (main_tum_ransac.cpp, main_tum_high_ransac.cpp) and the plotting script (plot_outlier.py) are included in this repository.

---

Citation

If you use this code in your research, please cite the corresponding manuscript:

@article{luo2026bapnp,
  title={Bapnp: a barycentric affine invariant linear solver for robust and efficient perspective-n-point pose estimation},
  author={Luo, Peilin and Guo, Yang},
  journal={The Visual Computer},
  volume={42},
  number={10},
  pages={450},
  year={2026},
  publisher={Springer}
}

---

1. MATLAB Simulations

The MATLAB code is located in the simulations/ directory. It includes the algorithm implementation, ablation studies, and comparisons with state-of-the-art methods.

1.1 Prerequisites & Setup

To run the comparisons, you need to download the baseline algorithms and add them to your MATLAB path:

1. MLPnP and other algorithms: Download from urbste/MLPnP_matlab_toolbox.
2. CPnP: Download from LIAS-CUHKSZ/CPnP-A-Consistent-PnP-Solver.
3. SRPnP: Download from (https://github.com/pingwangsky/PnP_tool)

Setup: Unzip these toolboxes and add their folders (and subfolders) to your MATLAB working path before running the experiments.

1.2 Core Algorithms

We provide unified interfaces for different solvers:

• BAPnP.m: Our proposed method (Linear Initialization + Gauss-Newton Refinement).
• BAPnP_Coplanar.m: Our proposed method
• pnp_linear_only.m: Our proposed method (Linear Initialization only).
• run_cpnp.m: Wrapper for the CPnP solver.
• (Other wrappers included in the folder)

1.3 Reproducing Paper Figures

Use the following scripts to reproduce the figures presented in the paper:

Figure in Paper	Description	MATLAB Script
Fig. 1	Geometric Comparison (Tetrahedron Volume)	Tetrahedron.m
Fig. 2	Ablation Studies	Ablation1.m, Ablation2.m
Fig. 3	Robustness to Image Noise	exp1.m
Fig. 4	Robustness to Point Density	exp2.m
Fig. 5	Computational Efficiency Plot	plot_time.m
Fig. 6	Quasi-Planar Stability & Spectral Gap Analysis	test_spectral_gap_comparison.m test_pnp_planarity_performance.m

---

2. C++ Implementation

The C++ source code is located in the src/ directory. It is designed for real-time performance evaluation and benchmark datasets.

2.1 Source Files

• src/bapnp.cpp: The C++ implementation of the BAPnP algorithm.
• main_benchmark.cpp: Runtime comparison against state-of-the-art implementations.
• main_colmap_benchmark.cpp: Evaluation on the South Building Dataset.
• main_tum.cpp: Raw evaluation on the TUM RGB-D Dataset (without outlier rejection).
• main_tum_ransac.cpp: RANSAC-integrated evaluation on the TUM RGB-D Dataset (500 iterations, 6-pt sampling, 2 px threshold).
• main_tum_high_ransac.cpp: RANSAC evaluation with synthetic extremal outlier injection (10%--50% ratios), testing robustness under adversarial periphery outliers.

2.2 Dataset Preparation

Before running the real-world benchmarks, please download the required datasets. Due to size constraints, they are not included in this repository.

1. South Building Dataset:

   • Download: Visit COLMAP Datasets and download "South Building".
   • Setup: Extract the dataset and ensure the path matches the configuration in main_colmap_benchmark.cpp .

2. TUM RGB-D Dataset:

   • Download: Visit TUM RGB-D Benchmark.
   • Sequence: We use the freiburg1_desk sequence for evaluation.
   • Setup: Download the sequence and place it in the working directory or update the path in main_tum.cpp.

2.3 Build and Run

Ensure you have a C++ compiler (supports C++11 or higher) and CMake installed.

Build:

mkdir build
cd build
cmake .. 
make -j

Runtime Benchmark:

./run_benchmark

TUM RGB-D Experiment:

./run_tum

TUM RANSAC Experiment:

./run_tum_ransac

TUM RANSAC with Extremal Outlier Injection:

./run_tum_high_ransac [outlier_ratio]
# e.g., ./run_tum_high_ransac 0.3  for 30% injected outliers

South Building (COLMAP) Experiment:

./run_colmap_bench